• Honam Mathematical Journal
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• v.33 no.4
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• pp.617-628
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• 2011

In relation to the classification of finite topological spaces the paper [17] studied various properties of finite topological spaces. Indeed, the study of future internet system can be very related to that of locally finite topological spaces with some order structures such as preorder, partial order, pretopology, Alexandroff topological structure and so forth. The paper generalizes the results from [17] so that the paper can enlarge topological and homotopic properties suggested in the category of finite topological spaces into those in the category of locally finite topological spaces including ALF spaces.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.12 no.4
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• pp.249-260
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• 2008

In this work we propose a mixed finite volume method for the Signorini problem which are based on the idea of Keller's finite volume box method. The triangulation may consist of both triangles and quadrilaterals. We choose the first-order nonconforming space for the scalar approximation and the lowest-order Raviart-Thomas vector space for the vector approximation. It will be shown that our mixed finite volume method is equivalent to the standard nonconforming finite element method for the scalar variable with a slightly modified right-hand side, which are crucially used in a priori error analysis.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.403-410
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• 2006

For a finite group G, #Cent(G) denotes the number of centralizers of its elements. A group G is called n-centralizer if #Cent(G) = n, and primitive n-centralizer if #Cent(G) = #Cent($\frac{G}{Z(G)}$) = n. The first author in [1], characterized the primitive 6-centralizer finite groups. In this paper we continue this problem and characterize the primitive 7-centralizer finite groups. We prove that a finite group G is primitive 7-centralizer if and only if $\frac{G}{Z(G)}{\simeq}D_{10}$ or R, where R is the semidirect product of a cyclic group of order 5 by a cyclic group of order 4 acting faithfully. Also, we compute #Cent(G) for some finite groups, using the structure of G modulu its center.

• Journal of Mechanical Science and Technology
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• v.15 no.11
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• pp.1499-1506
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• 2001

Various transition elements are used in general for the effective finite element analysis of complicated mechanical structures. In this paper, a solid-to-beam transition finite element, which can b e used for connecting a C1-continuity beam element to a continuum solid element, is proposed. The shape functions of the transition finite element are derived to meet the compatibility condition, and a transition element equation is formulated by the conventional finite element procedure. In order to show the effectiveness and convergence characteristics of the proposed transition element, numerical tests are performed for various examples. As a result of this study, following conclusions are obtained. (1) The proposed transition element, which meets the compatibility of the primary variables, exhibits excellent accuracy. (2) In case of using the proposed transition element, the number of nodes in the finite element model may be considerably reduced and the model construction becomes more convenient. (3) This formulation method can be applied to the usage of higher order elements.

• Smart Structures and Systems
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• v.5 no.5
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• pp.531-546
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• 2009

In the present analysis, the spline finite strip with higher-order shear deformation is formulated for the static analysis of piezoelectric composite plates. The proposed method incorporates Reddy's third-order shear deformation theory, Touratier's "Sine" model, Afaq's exponential model, Cho's higher-order zigzag laminate theory, as well as the classic plate theory and the first-order plate theory. Thus, the analysis can be conducted based on any of the above-mentioned theories. The selection of a specific method is done by simply changing a few terms in a 2 by 2 square matrix and the results, obtained according to different plate theories, can be compared to each other. Numerical examples are presented for piezoelectric composite plates subjected to mechanical loading. The results based on different shear deformation theories are compared with the three-dimensional solutions. The behaviours of piezoelectric composite plates with different length-to-thickness ratios, fibre orientations, and boundary conditions are also investigated in these examples.

• Bulletin of the Korean Mathematical Society
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• v.53 no.5
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• pp.1427-1437
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• 2016

Cauchy polynomials are also called Bernoulli polynomials of the second kind and these polynomials are very important to study mathematical physics. D. S. Kim et al. have studied some properties of Bernoulli polynomials of the second kind associated with special polynomials arising from umbral calculus. T. Kim introduced the degenerate Cauchy numbers and polynomials which are derived from the degenerate function $e^t$. Recently J. Jeong, S. H. Rim and B. M. Kim studied on finite times degenerate Cauchy numbers and polynomials. In this paper we consider finite times degenerate higher-order Cauchy numbers and polynomials, and give some identities and properties of these polynomials.

• Structural Engineering and Mechanics
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• v.27 no.1
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• pp.1-16
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• 2007

In the present study, a spline finite strip with higher-order shear deformation is formulated for the stability and free vibration analysis of composite plates. The analysis is conducted based on Reddy's third-order shear deformation theory, Touratier's "Sine" model, Afaq's exponential model and Cho's higher-order zigzag laminate theory. Consequently, the shear correction coefficients are not required in the analysis, and an improved accuracy for thick laminates is achieved. The numerical results, based on different shear deformation theories, are presented in comparison with the three-dimensional elasticity solutions. The effects of length-to-thickness ratio, fibre orientation, and boundary conditions on the critical buckling loads and natural frequencies are investigated through numerical examples.

• The Journal of the Acoustical Society of Korea
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• v.19 no.4
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• pp.84-92
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• 2000

In this paper, numerical scattering analysis for submerged scatterers is performed using finite and infinite elements. Unbounded domain is truncated into finite domain and finite elements are used in the domain. Infinite elements, So called Infinite Wave Envelope Elements (IWEE) which possess wave-like behavior, are used to take into account the infinite domain on the truncated boundary Scattering from rigid sphere is taken as an example and the effects of the order and mesh size of finite elements, size of finite element model and the order of IWEE are investigated. Quadratic finite element, refined mesh and higher order IWEE are recommended to improve the non-reflection boundary condition in the numerical scattering analysis.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.4 no.2
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• pp.135-142
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• 2000

We consider a multigrid algorithm for higher order finite difference scheme for the Poisson problem on rectangular domain. Several smoothers including Jacobi, Red-black Gauss-Seidel are tested and compared. Since higher order scheme gives much more accurate result then 5-point scheme, one may use small number of levels with higher order scheme and thus the overall cost is reduced quite a lot. The numerical experiment compares the two cases.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• v.9 no.1
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• pp.925-927
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• 2005

The study is about a finite field multiplying unit, which performs a calculation t-times as fast as the Mastrovito's multiplier architecture, suggesting and using the 2-times faster multiplier architecture. Former studies on finite field multiplication architecture includes the serial multiplication architecture, the array multiplication architecture, and the hybrid finite field multiplication architecture. Mastrovito's serial multiplication architecture has been regarded as the basic architecture for the finite field multiplication, and in order to exploit parallelism, as much resources were expensed to get as much speed in the finite field array multipliers. The array multiplication architecture has weakness in terms of area/performance ratio. In 1999, Parr has proposed the hybrid multipcliation architecture adopting benefits from both architectures. In the hybrid multiplication architecture, the main hardware frame is based on the Mastrovito's serial multiplication architecture with smaller 2-dimensional array multipliers as processing elements, so that its calculation speed is fairly fast costing intermediate resources. However, as the order of the finite field, complex integers instead of prime integers should be used, which means it cannot be used in the high-security applications. In this paper, we propose a different approach to devise a finite field multiplication architecture using Mastrovito's concepts.